Highest Common Factor of 754, 622, 749 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 754, 622, 749 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 754, 622, 749 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 754, 622, 749 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 754, 622, 749 is 1.
HCF(754, 622, 749) = 1
HCF of 754, 622, 749 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 754, 622, 749 is 1.
Highest Common Factor of 754,622,749 is 1
Step 1: Since 754 > 622, we apply the division lemma to 754 and 622, to get
754 = 622 x 1 + 132
Step 2: Since the reminder 622 ≠ 0, we apply division lemma to 132 and 622, to get
622 = 132 x 4 + 94
Step 3: We consider the new divisor 132 and the new remainder 94, and apply the division lemma to get
132 = 94 x 1 + 38
We consider the new divisor 94 and the new remainder 38,and apply the division lemma to get
94 = 38 x 2 + 18
We consider the new divisor 38 and the new remainder 18,and apply the division lemma to get
38 = 18 x 2 + 2
We consider the new divisor 18 and the new remainder 2,and apply the division lemma to get
18 = 2 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 754 and 622 is 2
Notice that 2 = HCF(18,2) = HCF(38,18) = HCF(94,38) = HCF(132,94) = HCF(622,132) = HCF(754,622) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 749 > 2, we apply the division lemma to 749 and 2, to get
749 = 2 x 374 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 749 is 1
Notice that 1 = HCF(2,1) = HCF(749,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 754, 622, 749 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 754, 622, 749?
Answer: HCF of 754, 622, 749 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 754, 622, 749 using Euclid's Algorithm?
Answer: For arbitrary numbers 754, 622, 749 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.